2016/11/09 by Maarten Wyns, Wyns, Maarten, Du Toit +2
Economics, Econometrics and Finance · #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Market Dynamics and Volatility #Monetary Policy and Economic Impact #Numerical Analysis (math.NA) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1611.02961
openalex publication_date 2016/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Calibration of stochastic local volatility (SLV) models to their underlying\nlocal volatility model is often performed by numerically solving a\ntwo-dimensional non-linear forward Kolmogorov equation. We propose a novel\nfinite volume (FV) discretization in the numerical solution of general 1D and\n2D forward Kolmogorov equations. The FV method does not require a\ntransformation of the PDE. This constitutes a main advantage in the calibration\nof SLV models as the pertinent PDE coefficients are often nonsmooth. Moreover,\nthe FV discretization has the crucial property that the total numerical mass is\nconserved. Applying the FV discretization in the calibration of SLV models\nyields a non-linear system of ODEs. Numerical time stepping is performed by the\nHundsdorfer-Verwer ADI scheme to increase the computational efficiency. The\nnon-linearity in the system of ODEs is handled by introducing an inner\niteration. Ample numerical experiments are presented that illustrate the\neffectiveness of the calibration procedure.\n